Asphericity and B\"okstedt-Neeman Theorem

TL;DR

This paper establishes a characterization of aspherical spaces through the B"{o}kstedt-Neeman Theorem, linking topological properties with derived categories of sheaves.

Contribution

It proves that a space is aspherical if and only if it satisfies the B"{o}kstedt-Neeman Theorem, providing a new categorical criterion for asphericity.

Findings

Topological spaces are aspherical iff they satisfy B"{o}kstedt-Neeman Theorem

Derived categories of locally constant sheaves are equivalent to those with locally constant cohomology in aspherical spaces

Provides a categorical characterization of asphericity

Abstract

We prove that a topological space is aspherical if and only if it satisfies B\"{o}kstedt-Neeman Theorem, i.e., the derived category of complexes of locally constant sheaves is equivalent to the derived category of complexes of sheaves with locally constant cohomology.